Is new Time Capsule max speed determined by slowest device on network?
No, the fastest device on the network would determine the max connection speed.
Or do all devices independently run at their fastest speeds (so one device can be on 802.11n, one on 802.11b, one on 802.11ac...).
Correct. If you have a large number of slow devices on the network, then they may pull things down a bit. If am using an 802.11n computer and add 2 old iPhones that only run at 802.11g speeds, the 802.11n devices are not affected at all.
If I get the new Time Capsule, is there really any benefit to upgrading from my years-old Time Capsule this (aside from 2TB of space instead of 1TB)?
While you will not realize the full benefit of the new 802.11ac Time Capsule unless you also have an 802.11ac computer, the 2 additional wireless antennas....total of 6 now, and higher antenna placement in the new Time Capsule should provide a bit better results with most of your devices.
My neighbor reports that his new Time Capsule just about doubled the range of his previous version Time Capsule and increased speeds 20-25% overall with his existing computers. We've seen similar posts from other users.
At the same time, we've also seen posts from users who do not report much improvement with their current devices.
So the bottom line to questions like yours has always been....and will always remain.....you will not know how a new product will perform in your home until you try it in your home.
You have a 14 day, no questions asked, return privilege from Apple if you want to try a new Time Capsule.